Rachel has an unknown sample of a radioisotope listed in the table. using a special technique, she is able to measure the mass of just the unknown isotope as 104.8 kg at 12: 02: 00 p. m. at 4: 11: 00 p. m. on the same day, the mass of the unknown radioisotope is 13.1 kg. which radioisotope is in the sample?

Barium-139

Explanation:

initial mass of the sample at 12:02:00 PM is given as

Mass of the sample at 4:11:00 PM is given as

so here since it is a sample of radioactive isotope so here we will say

now from above data we know that the time taken to reduce the mass is

now from above equation we will have

so here half life is given as

So here this isotope must be the one which will have half life of 1.4 hours

So it is nearly Barium-139

chemical energy --> gravitational potential energy --> kinetic energy --> elastic potential energy --> gravitational potential energy

explanation:

when emma starts the hike, the chemical energy stored in her body is used to climb up the mountain, and so she gains gravitational potential energy (because at the end, she will be at a higher height h above the ground). then she goes bungee jumping: as she falls, this gravitational potential energy is converted into kinetic energy (because her speed increases as she falls down), until the point when the rope stretches, and she stops moving. at that moment, all the kinetic energy is converted into elastic potential energy due to the stretching of the rope. then, this energy is released because the rope returns to its natural length, and emma gains a small increase in altitude , so she gains some gravitational potential energy.